Given $ m \angle RPS = 3x + 36$, and $ m \angle QPR = 6x + 135$, find $m\angle QPR$. $P$ $Q$ $S$ $R$
From the diagram, we see that together ${\angle QPR}$ and ${\angle RPS}$ form ${\angle QPS}$ , so $ {m\angle QPR} + {m\angle RPS} = {m\angle QPS}$ Since $\angle QPS$ is a straight angle, we know ${m\angle QPS = 180}$ Substitute in the expressions that were given for each measure: $ {6x + 135} + {3x + 36} = {180}$ Combine like terms: $ 9x + 171 = 180$ Subtract $171$ from both sides: $ 9x = 9$ Divide both sides by $9$ to find $x$ $ x = 1$ Substitute $1$ for $x$ in the expression that was given for $m\angle QPR$ $ m\angle QPR = 6({1}) + 135$ Simplify: $ {m\angle QPR = 6 + 135}$ So ${m\angle QPR = 141}$.